two similar solids have volumes V1 and V2 and corresponding sides of length x1 and x2. state the ratio V1;V2 in terms of x1 and x2.

Question

geometry of o levels

Answer 1

Let's say that we have a cube whose lengths are 1m each giving us a volume of 1*1*1=1m³. If we double the length of each side, we then have a cube with a volume2*2*2=8m³. So the ratio of the length of the sides of each cube is 1:2

while the volume is 1:8. If we triple the length of the sides of the first cube, we get a volume of 3*3*3=27m³. Giving us a ratio of 1:3 for side length and 1:27 for volume. 

 

As we can see, the relationship between 2 and 8 is 2³=8, and the relationship between 3 and 27 is 3³=27. So we cube the rate of change in the side length to get the rate of change in volume.

 

Giving out answer as x₁:x₂³